package org.matheclipse.core.integrate.rubi45;


import static org.matheclipse.core.expression.F.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctionCtors.*;
import static org.matheclipse.core.integrate.rubi45.UtilityFunctions.*;
import org.matheclipse.core.interfaces.IAST;

/** 
 * IndefiniteIntegrationRules from the <a href="http://www.apmaths.uwo.ca/~arich/">Rubi -
 * rule-based integrator</a>.
 *  
 */
public class IntRules72 { 
  public static IAST RULES = List( 
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,ASymbol,a,Tan(Plus(e,Times(f,x))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(Power(Times(d,n),-1),Int(Times(Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(n,Plus(Times(BSymbol,a),Times(ASymbol,b))),Times(Plus(Times(BSymbol,b,n),Times(ASymbol,a,Plus(n,C1))),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),RationalQ(n)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(ASymbol,a,Cot(Plus(e,Times(f,x))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(Power(Times(d,n),-1),Int(Times(Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(n,Plus(Times(BSymbol,a),Times(ASymbol,b))),Times(Plus(Times(BSymbol,b,n),Times(ASymbol,a,Plus(n,C1))),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),RationalQ(n)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_DEFAULT)),x_Symbol),
    Condition(Plus(Times(b,BSymbol,Tan(Plus(e,Times(f,x))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(n,C1)),-1)),Times(Power(Plus(n,C1),-1),Int(Times(Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Simp(Plus(Times(ASymbol,a,Plus(n,C1)),Times(BSymbol,b,n),Times(Plus(Times(ASymbol,b),Times(BSymbol,a)),Plus(n,C1),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),Not(And(RationalQ(n),LessEqual(n,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_DEFAULT)),x_Symbol),
    Condition(Plus(Times(CN1,b,BSymbol,Cot(Plus(e,Times(f,x))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(n,C1)),-1)),Times(Power(Plus(n,C1),-1),Int(Times(Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Simp(Plus(Times(ASymbol,a,Plus(n,C1)),Times(BSymbol,b,n),Times(Plus(Times(ASymbol,b),Times(BSymbol,a)),Plus(n,C1),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),Not(And(RationalQ(n),LessEqual(n,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),-1),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(b,-1),Int(Sec(Plus(e,Times(f,x))),x)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(b,-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),-1)),x))),And(FreeQ(List(a,b,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),-1),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(b,-1),Int(Csc(Plus(e,Times(f,x))),x)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(b,-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),-1)),x))),And(FreeQ(List(a,b,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Times(d,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(f,Plus(m,C1)),-1)),And(And(And(FreeQ(List(a,b,c,d,e,f,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Times(CN1,d,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(f,Plus(m,C1)),-1)),And(And(And(FreeQ(List(a,b,c,d,e,f,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(b,c),Times(CN1,a,d)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(a,f,Plus(Times(C2,m),C1)),-1)),Times(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))),Power(Times(a,b,Plus(Times(C2,m),C1)),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1))),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))))),RationalQ(m)),Less(m,CN1D2)))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(Plus(Times(b,c),Times(CN1,a,d)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(a,f,Plus(Times(C2,m),C1)),-1)),Times(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))),Power(Times(a,b,Plus(Times(C2,m),C1)),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1))),x))),And(And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))))),RationalQ(m)),Less(m,CN1D2)))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(d,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(f,Plus(m,C1)),-1)),Times(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))),Power(Times(b,Plus(m,C1)),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,f,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))))),Not(And(RationalQ(m),Less(m,CN1D2)))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(CN1,d,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(f,Plus(m,C1)),-1)),Times(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))),Power(Times(b,Plus(m,C1)),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,f,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))))),Not(And(RationalQ(m),Less(m,CN1D2)))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(d,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(f,Plus(m,C1)),-1)),Times(Power(Plus(m,C1),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Simp(Plus(Times(b,d,m),Times(a,c,Plus(m,C1)),Times(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Greater(m,C0)))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(CN1,d,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(f,Plus(m,C1)),-1)),Times(Power(Plus(m,C1),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Simp(Plus(Times(b,d,m),Times(a,c,Plus(m,C1)),Times(Plus(Times(a,d,m),Times(b,c,Plus(m,C1))),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Greater(m,C0)))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(Plus(Times(b,c),Times(CN1,a,d)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(f,Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1)),Times(Power(Times(Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Simp(Plus(Times(Plus(Times(a,c),Times(CN1,b,d)),Plus(m,C1)),Times(CN1,Plus(Times(c,b),Times(CN1,a,d)),Plus(m,C2),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(b,c),Times(CN1,a,d)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(f,Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1)),Times(Power(Times(Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Simp(Plus(Times(Plus(Times(a,c),Times(CN1,b,d)),Plus(m,C1)),Times(CN1,Plus(Times(c,b),Times(CN1,a,d)),Plus(m,C2),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),CN1D2),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Times(Sqrt(Plus(b,Times(a,Cos(Plus(e,Times(f,x)))))),Power(Times(Sqrt(Cos(Plus(e,Times(f,x)))),Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))))),-1),Int(Times(Plus(d,Times(c,Cos(Plus(e,Times(f,x))))),Power(Times(Power(Cos(Plus(e,Times(f,x))),QQ(3L,2L)),Sqrt(Plus(b,Times(a,Cos(Plus(e,Times(f,x))))))),-1)),x)),And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),CN1D2),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Times(Sqrt(Plus(b,Times(a,Sin(Plus(e,Times(f,x)))))),Power(Times(Sqrt(Sin(Plus(e,Times(f,x)))),Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))))),-1),Int(Times(Plus(d,Times(c,Sin(Plus(e,Times(f,x))))),Power(Times(Power(Sin(Plus(e,Times(f,x))),QQ(3L,2L)),Sqrt(Plus(b,Times(a,Sin(Plus(e,Times(f,x))))))),-1)),x)),And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Times(CN2,CSqrt2,c,Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Plus(c,Times(CN1,d,Sec(Plus(e,Times(f,x))))),Sqrt(Times(Plus(c,Times(d,Sec(Plus(e,Times(f,x))))),Power(c,-1))),Power(Times(d,f,Tan(Plus(e,Times(f,x))),Power(Times(c,Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Power(Plus(Times(a,c),Times(b,d)),-1)),m)),-1),AppellF1(C1D2,CN1D2,Negate(m),QQ(3L,2L),Times(Plus(c,Times(CN1,d,Sec(Plus(e,Times(f,x))))),Power(Times(C2,c),-1)),Times(b,Plus(c,Times(CN1,d,Sec(Plus(e,Times(f,x))))),Power(Plus(Times(b,c),Times(a,d)),-1)))),And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(Sqr(c),Negate(Sqr(d))))),Not(IntegerQ(Times(C2,m)))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Times(C2,CSqrt2,c,Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Plus(c,Times(CN1,d,Csc(Plus(e,Times(f,x))))),Sqrt(Times(Plus(c,Times(d,Csc(Plus(e,Times(f,x))))),Power(c,-1))),Power(Times(d,f,Cot(Plus(e,Times(f,x))),Power(Times(c,Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Power(Plus(Times(a,c),Times(b,d)),-1)),m)),-1),AppellF1(C1D2,CN1D2,Negate(m),QQ(3L,2L),Times(Plus(c,Times(CN1,d,Csc(Plus(e,Times(f,x))))),Power(Times(C2,c),-1)),Times(b,Plus(c,Times(CN1,d,Csc(Plus(e,Times(f,x))))),Power(Plus(Times(b,c),Times(a,d)),-1)))),And(And(And(And(FreeQ(List(a,b,c,d,e,f),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(Sqr(c),Negate(Sqr(d))))),Not(IntegerQ(Times(C2,m)))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(Plus(Times(b,c),Times(CN1,a,d)),Power(b,-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m)),x)),Times(d,Power(b,-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1))),x))),And(And(FreeQ(List(a,b,c,d,e,f,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(c_,Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),x_Symbol),
    Condition(Plus(Times(Plus(Times(b,c),Times(CN1,a,d)),Power(b,-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m)),x)),Times(d,Power(b,-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1))),x))),And(And(FreeQ(List(a,b,c,d,e,f,m),x),NonzeroQ(Plus(Times(b,c),Times(CN1,a,d)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(b,f,Plus(Times(C2,m),C1)),-1)),Times(Power(Times(Sqr(b),Plus(Times(C2,m),C1)),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Simp(Plus(Times(ASymbol,b,m),Times(CN1,a,BSymbol,m),Times(b,BSymbol,Plus(Times(C2,m),C1),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1D2)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(b,f,Plus(Times(C2,m),C1)),-1)),Times(Power(Times(Sqr(b),Plus(Times(C2,m),C1)),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Simp(Plus(Times(ASymbol,b,m),Times(CN1,a,BSymbol,m),Times(b,BSymbol,Plus(Times(C2,m),C1),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1D2)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),x_Symbol),
    Condition(Plus(Times(CN1,a,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(b,f,Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1)),Times(CN1,Power(Times(b,Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Simp(Plus(Times(b,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,C1)),Times(CN1,Plus(Times(a,ASymbol,b,Plus(m,C2)),Times(CN1,BSymbol,Plus(Sqr(a),Times(Sqr(b),Plus(m,C1))))),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),x_Symbol),
    Condition(Plus(Times(a,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(b,f,Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1)),Times(CN1,Power(Times(b,Plus(m,C1),Plus(Sqr(a),Negate(Sqr(b)))),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Simp(Plus(Times(b,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,C1)),Times(CN1,Plus(Times(a,ASymbol,b,Plus(m,C2)),Times(CN1,BSymbol,Plus(Sqr(a),Times(Sqr(b),Plus(m,C1))))),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),Sqr($($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),x_Symbol),
    Condition(Plus(Times(BSymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(b,f,Plus(m,C2)),-1)),Times(Power(Times(b,Plus(m,C2)),-1),Int(Times(Sec(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Simp(Plus(Times(b,BSymbol,Plus(m,C1)),Times(Plus(Times(ASymbol,b,Plus(m,C2)),Times(CN1,a,BSymbol)),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(FreeQ(List(a,b,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),Not(And(RationalQ(m),Less(m,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_DEFAULT),Sqr($($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),x_Symbol),
    Condition(Plus(Times(CN1,BSymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(b,f,Plus(m,C2)),-1)),Times(Power(Times(b,Plus(m,C2)),-1),Int(Times(Csc(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Simp(Plus(Times(b,BSymbol,Plus(m,C1)),Times(Plus(Times(ASymbol,b,Plus(m,C2)),Times(CN1,a,BSymbol)),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(FreeQ(List(a,b,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),Not(And(RationalQ(m),Less(m,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Times(CN1,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(m,n,C1))),ZeroQ(Plus(Times(a,ASymbol,m),Times(CN1,b,BSymbol,n)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Times(ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(m,n,C1))),ZeroQ(Plus(Times(a,ASymbol,m),Times(CN1,b,BSymbol,n)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(b,f,Plus(Times(C2,m),C1)),-1)),Times(Plus(Times(a,ASymbol,m),Times(b,BSymbol,Plus(m,C1))),Power(Times(Sqr(a),Plus(Times(C2,m),C1)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),n)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(m,n,C1))),RationalQ(m)),LessEqual(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(b,f,Plus(Times(C2,m),C1)),-1)),Times(Plus(Times(a,ASymbol,m),Times(b,BSymbol,Plus(m,C1))),Power(Times(Sqr(a),Plus(Times(C2,m),C1)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),n)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(m,n,C1))),RationalQ(m)),LessEqual(m,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(CN1,Plus(Times(a,ASymbol,m),Times(CN1,b,BSymbol,n)),Power(Times(b,d,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1))),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(m,n,C1))),Not(And(RationalQ(m),LessEqual(m,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(CN1,Plus(Times(a,ASymbol,m),Times(CN1,b,BSymbol,n)),Power(Times(b,d,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1))),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(m,n,C1))),Not(And(RationalQ(m),LessEqual(m,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Times(C2,b,BSymbol,Tan(Plus(e,Times(f,x))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(Times(C2,n),C1),Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))))),-1)),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Times(CN2,b,BSymbol,Cot(Plus(e,Times(f,x))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(Times(C2,n),C1),Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))))),-1)),And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),ZeroQ(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,ASymbol,Sqr(b),Tan(Plus(e,Times(f,x))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(a,f,n,Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))))),-1)),Times(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)),Power(Times(C2,a,d,n),-1),Int(Times(Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x)))))),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1))),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)))),RationalQ(n)),Less(n,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(ASymbol,Sqr(b),Cot(Plus(e,Times(f,x))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(a,f,n,Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))))),-1)),Times(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)),Power(Times(C2,a,d,n),-1),Int(Times(Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x)))))),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1))),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)))),RationalQ(n)),Less(n,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(C2,b,BSymbol,Tan(Plus(e,Times(f,x))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(Times(C2,n),C1),Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))))),-1)),Times(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)),Power(Times(b,Plus(Times(C2,n),C1)),-1),Int(Times(Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x)))))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n)),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)))),Not(And(RationalQ(n),Less(n,C0)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Sqrt(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN2,b,BSymbol,Cot(Plus(e,Times(f,x))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(Times(C2,n),C1),Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))))),-1)),Times(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)),Power(Times(b,Plus(Times(C2,n),C1)),-1),Int(Times(Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x)))))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n)),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),NonzeroQ(Plus(Times(ASymbol,b,Plus(Times(C2,n),C1)),Times(C2,a,BSymbol,n)))),Not(And(RationalQ(n),Less(n,C0)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,a,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(CN1,b,Power(Times(a,d,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,ASymbol,Plus(m,Negate(n),Negate(C1))),Times(CN1,b,BSymbol,n),Times(CN1,Plus(Times(a,BSymbol,n),Times(ASymbol,b,Plus(m,n))),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m,n)),Greater(m,C1D2)),Less(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(a,ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(CN1,b,Power(Times(a,d,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,ASymbol,Plus(m,Negate(n),Negate(C1))),Times(CN1,b,BSymbol,n),Times(CN1,Plus(Times(a,BSymbol,n),Times(ASymbol,b,Plus(m,n))),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m,n)),Greater(m,C1D2)),Less(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(b,BSymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(m,n)),-1)),Times(Power(Times(d,Plus(m,n)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Simp(Plus(Times(a,ASymbol,d,Plus(m,n)),Times(BSymbol,b,d,n),Times(Plus(Times(ASymbol,b,d,Plus(m,n)),Times(a,BSymbol,d,Plus(Times(C2,m),n,Negate(C1)))),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Greater(m,C1D2)),Not(And(RationalQ(n),Less(n,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,b,BSymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(m,n)),-1)),Times(Power(Times(d,Plus(m,n)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Simp(Plus(Times(a,ASymbol,d,Plus(m,n)),Times(BSymbol,b,d,n),Times(Plus(Times(ASymbol,b,d,Plus(m,n)),Times(a,BSymbol,d,Plus(Times(C2,m),n,Negate(C1)))),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Greater(m,C1D2)),Not(And(RationalQ(n),Less(n,CN1)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,d,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(a,f,Plus(Times(C2,m),C1)),-1)),Times(CN1,Power(Times(a,b,Plus(Times(C2,m),C1)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(ASymbol,a,d,Plus(n,Negate(C1))),Times(CN1,BSymbol,b,d,Plus(n,Negate(C1))),Times(CN1,d,Plus(Times(a,BSymbol,Plus(m,Negate(n),C1)),Times(ASymbol,b,Plus(m,n))),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m,n)),Less(m,CN1D2)),Greater(n,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(d,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(a,f,Plus(Times(C2,m),C1)),-1)),Times(CN1,Power(Times(a,b,Plus(Times(C2,m),C1)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(ASymbol,a,d,Plus(n,Negate(C1))),Times(CN1,BSymbol,b,d,Plus(n,Negate(C1))),Times(CN1,d,Plus(Times(a,BSymbol,Plus(m,Negate(n),C1)),Times(ASymbol,b,Plus(m,n))),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m,n)),Less(m,CN1D2)),Greater(n,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(b,f,Plus(Times(C2,m),C1)),-1)),Times(CN1,Power(Times(Sqr(a),Plus(Times(C2,m),C1)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Simp(Plus(Times(b,BSymbol,n),Times(CN1,a,ASymbol,Plus(Times(C2,m),n,C1)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,n,C1),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1D2)),Not(And(RationalQ(n),Greater(n,C0)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(b,f,Plus(Times(C2,m),C1)),-1)),Times(CN1,Power(Times(Sqr(a),Plus(Times(C2,m),C1)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Simp(Plus(Times(b,BSymbol,n),Times(CN1,a,ASymbol,Plus(Times(C2,m),n,C1)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Plus(m,n,C1),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Less(m,CN1D2)),Not(And(RationalQ(n),Greater(n,C0)))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),CN1D2),Sqrt(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(b,-1),Int(Times(Sqrt(Plus(a,Times(b,Sec(Plus(e,Times(f,x)))))),Sqrt(Times(d,Sec(Plus(e,Times(f,x)))))),x)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(b,-1),Int(Times(Sqrt(Times(d,Sec(Plus(e,Times(f,x))))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),CN1D2)),x))),And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),CN1D2),Sqrt(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))))),x_Symbol),
    Condition(Plus(Times(BSymbol,Power(b,-1),Int(Times(Sqrt(Plus(a,Times(b,Csc(Plus(e,Times(f,x)))))),Sqrt(Times(d,Csc(Plus(e,Times(f,x)))))),x)),Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(b,-1),Int(Times(Sqrt(Times(d,Csc(Plus(e,Times(f,x))))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),CN1D2)),x))),And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(BSymbol,d,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(f,Plus(m,n)),-1)),Times(d,Power(Times(b,Plus(m,n)),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(b,BSymbol,Plus(n,Negate(C1))),Times(Plus(Times(ASymbol,b,Plus(m,n)),Times(a,BSymbol,m)),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Greater(n,C1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,BSymbol,d,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Power(Times(f,Plus(m,n)),-1)),Times(d,Power(Times(b,Plus(m,n)),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,Negate(C1))),Simp(Plus(Times(b,BSymbol,Plus(n,Negate(C1))),Times(Plus(Times(ASymbol,b,Plus(m,n)),Times(a,BSymbol,m)),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Greater(n,C1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(CN1,Power(Times(b,d,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,ASymbol,m),Times(CN1,b,BSymbol,n),Times(CN1,ASymbol,b,Plus(m,n,C1),Sec(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Less(n,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(CN1,Power(Times(b,d,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,ASymbol,m),Times(CN1,b,BSymbol,n),Times(CN1,ASymbol,b,Plus(m,n,C1),Csc(Plus(e,Times(f,x))))),x)),x))),And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(n)),Less(n,C0)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(b,-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),m),Power(Times(d,Sec(Plus(e,Times(f,x)))),n)),x)),Times(BSymbol,Power(b,-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Sec(Plus(e,Times(f,x)))),n)),x))),And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)),Power(b,-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),m),Power(Times(d,Csc(Plus(e,Times(f,x)))),n)),x)),Times(BSymbol,Power(b,-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,C1)),Power(Times(d,Csc(Plus(e,Times(f,x)))),n)),x))),And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,m),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),ZeroQ(Plus(Sqr(a),Negate(Sqr(b))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,a,ASymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(Power(Times(d,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C2))),Power(Times(d,Sec(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,Plus(Times(a,BSymbol,n),Times(CN1,ASymbol,b,Plus(m,Negate(n),Negate(C1))))),Times(Plus(Times(C2,a,b,BSymbol,n),Times(ASymbol,Plus(Times(Sqr(b),n),Times(Sqr(a),Plus(C1,n))))),Sec(Plus(e,Times(f,x)))),Times(b,Plus(Times(b,BSymbol,n),Times(a,ASymbol,Plus(m,n))),Sqr(Sec(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m,n)),Greater(m,C1)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(a,ASymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,n),-1)),Times(Power(Times(d,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C2))),Power(Times(d,Csc(Plus(e,Times(f,x)))),Plus(n,C1)),Simp(Plus(Times(a,Plus(Times(a,BSymbol,n),Times(CN1,ASymbol,b,Plus(m,Negate(n),Negate(C1))))),Times(Plus(Times(C2,a,b,BSymbol,n),Times(ASymbol,Plus(Times(Sqr(b),n),Times(Sqr(a),Plus(C1,n))))),Csc(Plus(e,Times(f,x)))),Times(b,Plus(Times(b,BSymbol,n),Times(a,ASymbol,Plus(m,n))),Sqr(Csc(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m,n)),Greater(m,C1)),LessEqual(n,CN1)))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§sec"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(b,BSymbol,Tan(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(m,n)),-1)),Times(Power(Plus(m,n),-1),Int(Times(Power(Plus(a,Times(b,Sec(Plus(e,Times(f,x))))),Plus(m,Negate(C2))),Power(Times(d,Sec(Plus(e,Times(f,x)))),n),Simp(Plus(Times(Sqr(a),ASymbol,Plus(m,n)),Times(a,b,BSymbol,n),Times(Plus(Times(a,Plus(Times(C2,ASymbol,b),Times(a,BSymbol)),Plus(m,n)),Times(Sqr(b),BSymbol,Plus(m,n,Negate(C1)))),Sec(Plus(e,Times(f,x)))),Times(b,Plus(Times(ASymbol,b,Plus(m,n)),Times(a,BSymbol,Plus(Times(C2,m),n,Negate(C1)))),Sqr(Sec(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Greater(m,C1)),Not(And(And(IntegerQ(n),Greater(n,C1)),Not(IntegerQ(m))))))),
ISetDelayed(Int(Times(Plus(A_,Times(B_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),Power(Plus(a_,Times(b_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_))))),m_),Power(Times(d_DEFAULT,$($s("§csc"),Plus(e_DEFAULT,Times(f_DEFAULT,x_)))),n_)),x_Symbol),
    Condition(Plus(Times(CN1,b,BSymbol,Cot(Plus(e,Times(f,x))),Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C1))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Power(Times(f,Plus(m,n)),-1)),Times(Power(Plus(m,n),-1),Int(Times(Power(Plus(a,Times(b,Csc(Plus(e,Times(f,x))))),Plus(m,Negate(C2))),Power(Times(d,Csc(Plus(e,Times(f,x)))),n),Simp(Plus(Times(Sqr(a),ASymbol,Plus(m,n)),Times(a,b,BSymbol,n),Times(Plus(Times(a,Plus(Times(C2,ASymbol,b),Times(a,BSymbol)),Plus(m,n)),Times(Sqr(b),BSymbol,Plus(m,n,Negate(C1)))),Csc(Plus(e,Times(f,x)))),Times(b,Plus(Times(ASymbol,b,Plus(m,n)),Times(a,BSymbol,Plus(Times(C2,m),n,Negate(C1)))),Sqr(Csc(Plus(e,Times(f,x)))))),x)),x))),And(And(And(And(And(FreeQ(List(a,b,d,e,f,ASymbol,BSymbol,n),x),NonzeroQ(Plus(Times(ASymbol,b),Times(CN1,a,BSymbol)))),NonzeroQ(Plus(Sqr(a),Negate(Sqr(b))))),RationalQ(m)),Greater(m,C1)),Not(And(And(IntegerQ(n),Greater(n,C1)),Not(IntegerQ(m)))))))
  );
}
